Method for trimming resistors

ABSTRACT

There is provided a method and circuit for trimming a functional resistor on a thermally isolated micro-platform such that a second functional resistor on the same micro-platform remains substantially untrimmed; a method and circuit for providing and trimming a circuit such that at least two circuit elements of the circuit are subjected to a same operating environment and the operating environment is compensated for by distributing heat generated during operation of the circuit among the two circuit elements; a method and circuit for trimming a functional resistor on a thermally-isolated micro-platform such that a constant temperature distribution is obtained across the functional resistor; and a method and circuit for calculating a temperature coefficient of resistance of a functional resistor.

FIELD OF THE INVENTION

[0001] The invention relates to the trimming of a resistor or resistors,suitable for use at any level of the manufacturer-to-user chain. Morespecifically, it relates to trimming by resistive heating using electriccurrent in the resistor itself or in an adjacent resistor.

BACKGROUND OF THE INVENTION

[0002] The trimming (adjustment) of resistors is a widely used procedurein the manufacture of microelectronics and electronic components, and incommon design of user circuits, especially where precision calibrationis desired. In principle, one trims the resistor until an observablelocal or global circuit parameter reaches a desired value. Resistortrimming is widespread in both manufacturing of a variety of componentsand instruments, and in the user community.

[0003] Several methods exist for trimming resistors, applicable atvarious levels of the manufacturer-to-user chain, includinglaser-trimming, electrical trimming, trimming by reconfiguration ofresistor networks using fuses, and the use of trimpots (potentiometers)having variable numbers of resistive turns.

[0004] Electro-thermal trimming phenomena have been observed by severalauthors, for the trimming of a variety of resistor materials. Forexample, Kato and Ono (“Constant Voltage Trimming of Heavily-DopedPolysilicon Resistors,” Jpn. J. Appl. Phys. Vol. 34, 1995, pp.45-53),related experimental results to a theoretical model, whereby theinstability of polysilicon as a function of applied voltage and currentwere explained by melting-segregation at grain boundaries in thepolysilicon, modified by the temperature dependence of grain resistance.In their formulation, the resistance behavior is found to be highlynon-linear, with little or no change in resistance for low powerdissipation (below a certain threshold), and dramatically increasedinstability above a certain threshold. Also, research at Motorola by D.Feldbaumer, J. Babcock, (“Theory and Application of Polysilicon ResistorTrimming”, Solid-State Electronics, 1995, vol. 38, pp. 1861-1869) provethat polysilicon resistors, so-trimmed at higher temperature(s), exhibitexcellent stability in absolute resistance, during operation at or nearroom temperature.

[0005] The thermal instability, (unstable resistance variation withtemperature) of polysilicon resistors located on micro-machined platformsuspended over cavities, is known (Canadian Microelectronics CorporationReport #IC95-08 September 1995; and O. Grudin, R. Marinescu, L. M.Landsberger, D. Cheeke, M. Kahrizi, “CMOS-Compatible High-TemperatureMicro-Heater: Microstructure Release and Testing,” Canadian Journal ofElec. and Comp. Engineering, 2000, Vol.25, No.1, pp.29-34.) It is knownthat, for a resistance element on a micro-platform, the resistance couldbe increased or decreased depending on the power applied through thatresistance element. This is usually considered to be a disadvantage forthe use of polysilicon for resistive elements where stability isimportant. This present invention concerns the use of this instability(or any similar threshold-dependent instability in resistive materials),to overcome any of a group of several obstacles present in the aggregateof the prior art. In particular, the material should be stable below acertain threshold of temperature or power dissipation, and relativelyless stable above such a threshold, such that its resistance can bemodified.

[0006] There exists electrical trimming of metal resistors based oninducing electro-migration in the resistive elements by pulsing highcurrents (U.S. Pat. Nos. 4,870,472, 4,606,781). This method relies onvery high current density to cause the electro-migration.

[0007] There exists electrical trimming based on thermally-inducedchanges in resistivity of polysilicon resistors residing on a substrate(U.S. Pat. No. 4,210,996; D. Feldbaumer, J. Babcock,. V. Mercier, C.Chun, “Pulse Current Trimming of Polysilicon Resistors”, IEEE Trans.Electron Devices, 1995, vol. 42, pp. 689-695; D. Feldbaumer, J. Babcock,“Theory and Application of Polysilicon Resistor Trimming”, Solid-StateElectronics, 1995, vol. 38, pp. 1861-1869), or resistors made from otherthermally-mutable types of materials). This method relies on theapplication of highly dissipated power (such as several watts), tosufficiently heat the resistors while they are on the substrate whicheffectively acts as a heat-sink. This in turn requires high voltage andbrings the danger of damage from electrostatic discharge (ESD).

[0008] Arguably in large part to get around this problem, Motorolainvented thermal trimming of a functional resistor by an auxiliaryresistor which is electrically-isolated from the functional resistor.This allows functional trimming to set a parameter of a larger circuit(U.S. Pat. Nos. 5,679,275, 5,635,893, 5,466,484), with the trimmableresistor as a component, without repeated disconnection-reconnection ofthe functional resistor. This also allows the trimming of resistorshaving high resistance values, without extra constraints on the heaterresistor.

[0009] The Motorola invention involves placing the resistors one overthe other, separated by a very thin electrically-insulating film. Thisconfiguration is required principally because the two resistors aresituated on the substrate, which acts as a heat sink. Thus, asubstantial amount of power is required to be dissipated to attain thetrimming temperature. Consequently, the one-over-the-other configurationis preferred in the prior art, in order to maximize the heat transferredfrom the heater-resistor to the functional-resistor. Any otherconfiguration, such as side-by-side and made from the same depositedlayer, would require much higher power-dissipation in theheater-resistor, which in turn would require a higher supply voltage andwould unduly heat the substrate. It should be noted that the substantialpower dissipated in the heater resistor must be conducted away throughthe insulating oxide, functional resistor, and other surrounding layersand devices.

[0010] The concept of a micro-platform or microstructure suspended overa cavity in a substrate (such as a cavity micro-machined in silicon),including electrically-resistive elements for heating and/or sensing,has been well-known in the literature for a decade or more (CanadianMicroelectronics Corporation Report #IC95-08 September 1995; F. Volkleinand H. Baltes, “A Microstructure for Measurement of Thermal Conductivityof Polysilicon Thin Films”, J. Microelectromechanical Systems, Vol.1,No.4, December 1992, p.193, and references therein; Y. C. Tai and R. S.Muller, “Lightly-Doped Polysilicon Bridge as an Anemometer,” Transducers'87, Rec. of the 4th International Conference on Solid-State Sensors andActuators 1987, pp.360-363; N. R. Swart and A. Nathan, “ReliabilityStudy of Polysilicon for Micro-hotplates,” Solid State Sensor andActuator Workshop, Hilton Head, Jun. 13-16, 1994, pp.119-122.).Micro-platforms with embedded resistive elements are commonly seen inmicro-sensor, micro-actuator and micro-electromechanical systems (MEMS)literature since 1990 or earlier (e.g. I. H. Choi and K. Wise, “ASilicon-Thermopile-Based Infrared Sensing Array for Use in AutomatedManufacturing,” IEEE Transactions on Electron Devices, vol. ED-33, No.1,pp.72-79, January 1986).

[0011] The concept of using a resistive heater to heat an entiresuspended micro-platform or microstructure is also well-known in theliterature for at least approximately a decade (C. H. Mastrangelo, J.H.-L. Yeh, R. S. Muller, “Electrical and Optical Characteristics ofVacuum-Sealed Polysilicon Micro-lamps”, IEEE Trans. Electron. Dev.,vol.39, No.6, June 1992, pp. 1363-1375; N. R. Swart, and A. Nathan,“Reliability of Polysilicon for Micro-plates,” Solid-State Sensor andActuators Workshop, Hilton Head, South California, Jun. 13-16, 1994, pp.119-122; S. Wessel, M. Parameswaran, R. F. Frindt, and R. Morrison, “ACMOS Thermally-isolated Heater Structure as Substrate for SemiconductorGas Sensors,” Microelectronics, Vol.23, No.6, September 1992,pp.451-456; M. Parameswaran, A. M. Robinson, Lj. Ristic, K. C. Chau, andW. Allegretto, “A CMOS Thermally Isolated Gas Flow Sensor,” Sensors andMaterials, 2, 1, (1990), pp. 17-26.)

[0012] University of Michigan has patented (U.S. Pat. No. 6,169,321),the thermally-induced modification of parameters such as resonancefrequency and Q of micro-machined resonators and other micro-structuresresiding on a micro-platform, using a separate micro-heater, also on themicro-platform.

[0013] Thermal trimming of a thermo-anemometer-type of sensor (such as athermal accelerometer) is known (U.S. Pat. No. 5,808,197), wheretemperature-sensitive metal resistors are heated until they oxidize,hence changing the resistance of the metal film. This procedure is notreversible, and can be used only at the manufacturing stage (notpractical for user- or field-trimming).

[0014] A method of creating a precise resistance having little-to-nodrift with temperature (so-called “zero-TCR”), based on combination(connection) of two resistors having positive and negative temperaturecoefficients of resistance (TCR's), with subsequent laser trimming, hasalso been invented (U.S. Pat. No. 6,097,276). The method involvescalibration steps wherein the resistor is heated up to a predeterminedtemperature (T), then the T-induced resistance drift is measured, thenthe structure is laser-trimmed to minimize net TCR of the combinedresistor, and then the process is repeated until the TCR is reduced tothe desired level.

[0015] The inclusion of trimmable resistors in certain devices andapplications has also been considered in prior inventions (U.S. Pat.Nos. 5,679,275, 5,635,893, 5,466,484). In particular, the use in opamps, in reference voltage sources, and in digital-to-analog convertorsand analog-to-digital convertors (DAC/ADC's) has been outlined (U.S.Pat. Nos. 5,679,275, 5,635,893, 5,466,484.)

[0016] There is a need for highly accurate trimming that can exceed theaccuracy achieved by laser trimming and does not require specialequipment such as powerful lasers.

SUMMARY OF THE INVENTION

[0017] Accordingly, an object of the present invention is to performeffective trimming of functional resistors made from unstable material,wherein the trimming behavior depends sensitively on temperature above acertain threshold, by obtaining a temperature relatively constant withtime in the targeted element, and by obtaining a relatively flat spatialtemperature profile in the targeted element. This should lead to theeffective trimming of resistors in a wider range of devices, and in awider range of circumstances, and the enabling of practicaluser-trimming and field-trimming of applications devices such asresistor dividers, trimpots, resistor networks, op-amps, instrumentationop-amps, reference voltage sources, DAC/ADC's, signal conditioningcircuits, programmable-gain amplifiers, piezoresistors, and sensors.

[0018] It is also an object of the present invention to independentlytrim functional elements, such as resistors, while maintaining them inclose thermal contact.

[0019] It is also an object of the present invention to reduce theamount of power needed to accomplish trimming.

[0020] It is also an object of the present invention to trim afunctional element, such as a resistor, wherein a desired output signaldepends critically on the interactive response of at least twofunctional independently trimmable elements.

[0021] According to a first broad aspect of the present invention, thereis provided a method for trimming a functional resistor, the methodcomprising: providing a thermally-isolated micro-platform on asubstrate; placing a plurality of thermally-trimmable functionalresistors on the thermally-isolated micro-platform; subjecting a portionof the thermally-isolated micro-platform to a heat pulse such that aresistance value of one of said plurality of functional resistors istrimmed while a resistance value of remaining ones of said plurality offunctional resistors remains substantially untrimmed.

[0022] Preferably, pulse-heating is intended to heat a sub-region of thethermally-isolated plate. Here, it is intended for the heat dissipation(or the bulk of the heat dissipation) to be localized within arelatively small portion (containing the heat-targeted region orregions, which may be areas or volumes) of a thermally-isolated platewithout affecting other elements on the plate. Four types of pulses(steady-state square pulse, quasi-static square pulse, dynamic squarepulse, and dynamic shaped pulse) are to be used in this particular mode(heating a sub-region of the thermally-isolated plate).”

[0023] In addition to this mode, the other two potential heatlocalization modes relative to heat dissipation in the zones surroundingthe heat-targeted regions are the “sub-region on substrate” and the“thermally-isolated plate”. In the sub-region on substrate, it isintended for the heat dissipation (or the bulk of the heat dissipation)to be localized within a sub-region (containing the heat-targetedregion) of a device, where that sub-region is simply located on asubstrate, usually a semiconductor substrate. The heat-targeted regionmay be directly on the substrate, or supported or separated from themain substrate by thin films, which may be insulating. In thethermally-isolated plate, it is intended for the heat dissipation (orthe bulk of the heat dissipation) to be localized within a relativelythermally-isolated plate containing the heat-targeted region. The plateis relatively well thermally isolated from a main substrate, usually asemiconductor substrate. One way to accomplish this thermal isolation isto make the plate suspended over a cavity in the substrate. The platemay often be composed of various layers, such as insulators orconductors or semiconductors, as long as the overall thermal isolationis substantial. Essentially, all three heat localization modes can beused with a dynamic shaped pulse.

[0024] According to a second, broad aspect of the present invention,there is provided a method for providing and trimming a circuit, themethod comprising: providing at least one thermally-isolatedmicro-platform on a substrate; placing at least two resistive elementswith non-zero temperature induced drift on said at least onethermally-isolated micro-platform, such that said at least two resistiveelements on said at least one micro-platform are subjected to asubstantially same operating environment, at least one of said at leasttwo resistive elements on said at least one micro-platform beingthermally trimmable; trimming said at least one resistive element onsaid at least one micro-platform to trim said circuit by thermalcycling; connecting said at least two resistive elements together insaid circuit in a manner to compensate for said operating environment onsaid at least one micro-platform; wherein heat generated duringoperation on the at least one micro-platform is distributed among saidat least two resistive elements such that temperature drift issubstantially compensated.

[0025] According to a third broad aspect of the present invention, thereis provided a method for trimming a functional resistor, the methodcomprising: providing a thermally-isolated micro-platform on asubstrate; placing a functional resistor on said thermally-isolatedmicro-platform; subjecting said functional resistor to a heat sourcehaving a power dissipation geometry adapted to obtain a substantiallyconstant temperature distribution across said functional resistor when atemperature of said functional resistor is raised for trimming purposes;and trimming said functional resistor using at least one heat pulse.

[0026] According to a fourth broad aspect of the present invention,there is provided a circuit for trimming a functional resistor, thecircuit comprising: a thermally-isolated micro-platform on a substrate;a plurality of functional resistors spaced apart on thethermally-isolated micro-platform; and trimming circuitry for subjectinga portion of the thermally-isolated micro-platform to heat pulses suchthat a resistance value of one of said plurality of functional resistorsis trimmed while a resistance value of remaining ones of said pluralityof functional resistors remains substantially untrimmed.

[0027] According to a fifth broad aspect of the present invention, thereis provided a circuit for trimming circuit elements, the circuitcomprising: at least one thermally-isolated micro-platform on asubstrate; at least two resistive elements with non-zero temperatureinduced drift on said at least one thermally-isolated micro-platform,such that said at least two resistive elements on said at least onemicro-platform are subjected to a substantially same operatingenvironment, at least one of said at least two resistive elements onsaid at least one micro-platform being thermally trimmable; and trimmingcircuitry for thermally trimming said at least one of said at least tworesistive elements; wherein said at least two resistive elements areconnected together in said circuit in a manner to compensate for saidoperating environment on said at least one micro-platform, and heatgenerated on the at least one micro-platform is distributed among the atleast two circuit elements such that an effect of temperature drift iscompensated.

[0028] According to a sixth broad aspect of the present invention, thereis provided a circuit for trimming a functional resistor, the circuitcomprising: a thermally-isolated micro-platform on a substrate; afunctional resistor on said thermally-isolated micro-platform subject toa heat source having a power dissipation geometry adapted to obtain asubstantially constant temperature distribution across said functionalresistor when a temperature of said functional resistor is raised fortrimming purposes; and trimming circuitry for trimming the functionalresistor.

[0029] According to a seventh broad aspect of the present invention,there is provided a method for calculating a temperature coefficient ofresistance of a functional resistor, the method comprising: providing atleast one thermally-isolated micro-platform on a substrate; placing afunctional resistor on said at least one thermally-isolatedmicro-platform; heating said functional resistor; measuring a resistancevalue of said functional resistor at ambient temperature and at anelevated temperature; and calculating said temperature coefficient ofresistance based on said measured resistance values.

[0030] According to an eighth broad aspect of the present invention,there is provided a circuit for calculating a temperature coefficient ofresistance of a functional resistor, the circuit comprising: at leastone thermally-isolated micro-platform on a substrate; a functionalresistor on said at least one thermally-isolated micro-platform; heatingcircuitry for heating said functional resistor; measuring circuitry formeasuring a resistance value of said functional resistance at ambienttemperature and at an elevated temperature; and calculating circuitryfor calculating said temperature coefficient of resistance based on saidresistance value at ambient temperature and at an elevated temperature.

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] These and other features, aspects and advantages of the presentinvention will become better understood with regard to the followingdescription and accompanying drawings wherein:

[0032]FIG. 1 depicts graphs of temperature vs. time, illustratingdifferent pulse heating modes relative to the temperature attained inthe heat-targeted region;

[0033]FIG. 2 is a top view schematic of a possible configuration of themicro-platform with four resistors, suspended over a cavity;

[0034]FIG. 3 is a cross-sectional view of the structure shown in FIG. 2;

[0035]FIG. 4 shows schematically one potential layout of two pairs offunctional and heating resistors on the micro-platform withcorresponding temperature distributions under transient and statictemperature conditions;

[0036]FIG. 5 shows schematically one potential layout of amicro-platform, similar to FIG. 4, with a plurality of slots;

[0037]FIG. 6 shows schematically one potential layout of amicro-platform, similar to FIGS. 4, 5, with continuous slots;

[0038]FIG. 7 is a view of the electrical contacts entering one of thebridges of the micro-platform, for immunity to thermal gradients on thesubstrate;

[0039]FIG. 8 shows schematically one possible layout of an R-2R divider,arranged on a single micro-platform;

[0040]FIG. 9 shows an example of pairs of resistors on separate closelyproximal micro-platforms;

[0041]FIG. 10 shows an example of pairs of resistors on separate closelyproximal micro-plafforms with bridges and connections arranged to beimmune to thermal gradients on the substrate;

[0042]FIG. 11 shows schematically an example of a layout of a trimmableR-2R divider on separate micro-plafforms (or single microplatform withcontinuous slot);

[0043]FIG. 12 shows three examples of layouts intended to dissipate morepower at the edges of the heat-targeted region;

[0044]FIG. 13 is an example of a configuration allowing time-varyingthermal isolation;

[0045]FIG. 14 shows the electrical schematic of two functionalresistors, and two heating resistors electrically isolated from thefunctional resistors;

[0046]FIG. 15 shows a possible embodiment for a trimmable thermal sensor(e.g. thermo-anemometer or thermal accelerometer), arranged on a singlemicro-platform with a slot;

[0047]FIG. 16 shows a possible embodiment of a thermal sensor (e.g.thermo-anemometer or thermal accelerometer), arranged on a plurality ofmicro-platforms;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0048] It should be noted that for the purpose of this disclosure,trimming is to be understood as increasing or decreasing theroom-temperature resistance value of a resistor. It should also be notedthat thermally-isolated is meant to describe an element that is isolatedfrom other elements such that the heat flux (proportional to temperaturedifferential) generated between the element and other elements, isgenerally low. Electrically-isolated is meant to describe an elementthat is isolated from other elements such that the resistance betweenthis element and other elements is very high (e.g. hundreds of k-ohms).The term signal is meant to describe any data or control signal, whetherit be an electric current, a light pulse, or any equivalent.Furthermore, obtaining a constant or flat temperature distribution,T(x), is equivalent to a relatively flat or substantially constanttemperature distribution across a resistor. The entire resistance cannotbe at the same temperature since a portion of the resistor must be offthe micro-platform (due to the continuous nature of resistors) andelectrical contacts must be at a lower temperature. Therefore, obtaininga substantially constant temperature distribution across a resistor isunderstood to mean across a maximum possible fraction of the resistor. Apulse is to be understood as a short duration of current flow.

[0049] To underlie the invention herein, an outline and discussion ofcertain modes of heating and heat localization is in order. Thermal andelectro-thermal trimming of a resistor involves the application of heatto a target resistor for a certain time-period. Thus, almost bydefinition, all such purposeful trimming is done by a heat pulse orpulses. If the behavior of the resistor is well-known and highlypredictable, effective trimming can be done with a single well-designedpulse. If not, or if greater precision is desired, an adaptive series ofpulses can be applied. In general, such pulses may have simple shape(e.g. square), or more complicated shape, depending on the desiredvariation of heating behavior with time.

[0050] Also, since such trimming usually targets a particular resistiveelement localized in a certain sub-volume or sub-area of a larger(usually integrated) device, (which usually must maintain its operatingtemperature within certain narrow ranges), the localization of the heatin and around the target elements may be of considerable importance.Specifically, the time-variation and spatial variation of heating in thetarget element(s) may be very important in the attainment of the desiredtrimming result, which will be strongly influenced by the combination ofpulse and heat localization characteristics.

[0051] These will be particularly important in light of the highlynon-linear nature of trimming. For example, both the degree of trimmingand whether the resistance of a resistive element is increased ordecreased (trimmed up vs. down), may depend very sensitively on theactual instantaneous temperature of the resistive element. Thus,accurate and efficient trimming may depend critically on very precisecontrol of the time- and spatial variation of the heating, and thereforeon pulse and heat localization modes. A range of cases are of particularinterest in this invention, outlined and discussed below.

[0052] The situation depicted in FIG. 1.a is when a square pulse is usedand the heat-targeted element attains thermal steady-state with thesurroundings for a substantial portion of the pulse (e.g. within 2% forgreater than 90% of the pulse duration). While the spatial profile mayvary with position within or surrounding the heat-targeted region, thisT(x) profile becomes constant with time, after an initial transient,Δt_(ss) which is substantially shorter than the duration of the squarepulse, Δt_(p). This type of pulse is called a steady-state square pulse.

[0053] The situation depicted in FIG. 1.b is again a square pulse, andthe heat-targeted region attains some measure of equilibration with thesurroundings, within some more-relaxed factor like 10% of thesteady-state value, for some significant fraction (e.g. ½) of the pulseduration. This is a similar principle to (a) above, but can be used incases where the requirement of accuracy of temperature control is not asstringent. This type of pulse is called a quasi-static square pulse.

[0054] The situation depicted in FIG. 1.c represents a square pulse,where the pulse duration Δt_(p), is much less than the time constant,Δt_(ss), for achieving steady-state heat distribution in and around theheat-targeted region. The heat-targeted region experiences only a rapidrise and fall of temperature, without equilibration. This type of pulseis called a dynamic square pulse.

[0055] In view of the lack of temperature equilibration in FIG. 1cabove, the pulse may be shaped for the purpose of making theinstantaneous (elevated) temperature constant with time in theheat-targeted region. Again, the pulse duration Δt_(p), is much lessthan the time constant, Δt_(ss), for equilibration, but here thepulse-shape is designed to achieve a relatively flat time-behavior,except for rapid turn-on and turn-off transients. An example of thissituation is depicted in FIG. 1.d, illustrating a dynamic shaped pulse.

[0056] In DC/quasi-static and steady-state trimming, one may userelatively long trimming pulses, such as 100 ms and longer, and theheated microstructure may or may not be relatively uniformly andentirely heated by those pulses. If one models the heated microstructureas being uniformly and entirely heated by those pulses, then one canestimate a maximum reasonable power P_(max) for many applications to beP=IV=I²R=V²/R=P_(max)=100 mW. For example, this could correspond toR_(heater)=500Ω, (relatively low), I=15 mA, V=7.5 V, (low enough formany user devices). With these parameters, in order to reach an elevatedtemperature of 500° C.-700° C., (roughly realistic in the case ofthermally-trimmed resistors), the microstructure must have thermalisolation higher than 5-7° K/mW. The numerical analysis above is alsovalid for the case of a sub-region of the microstructure being heated.The geometry, materials, and layout of the structure must be properlydesigned to meet this requirement. For example, in a device based on asuspended microstructure, this translates to constraints on suchparameters as length and width of supporting bridges, thickness, thermalconductivity of the layers making up the microstructure, depth of thecavity.

[0057] In pulse-based trimming within this invention, one uses pulsesshort enough to heat certain localized areas of a particularmicrostructure, without affecting nearby areas on the samemicrostructure (or another nearby microstructure). In order for pulsetrimming to be practically effective, again the trimming power must notbe too high, for the same user-based restrictions, and there is theadded restriction that the thermal conductivity within themicrostructure itself must not be too high. This in turn restricts suchparameters as the thickness, h, of the microstructure (assuming that itis of generally planar shape). A single trimming pulse having energyE=PΔt must heat an area A_(h) of the suspended microstructure havingthickness h, up to above the trimming temperature T_(trim) defined byequation:$T_{trim} = {\frac{P\quad \Delta \quad t}{c_{v}{\rho \left( V_{h} \right)}}.}$

[0058] The heated volume V_(h) can be described as (A_(h)h), where A_(h)is the effective area of the heated region. Since heat diffusion hascharacteristic length L_(hd)={square root}{square root over (2χΔt)}(where thermal diffusivity χ=k/ρc_(v); k is thermal conductivity; ρ isdensity and c_(v) is specific heat of the material of themicrostructure), the heated area A_(h)=(πL_(hd) ²+A_(R)), where A_(R) isthe area of the heater resistor. Therefore, if the area of the heaterresistor is neglected,$T_{trim} = {\frac{P}{2\quad \pi \quad k\quad h}.}$

[0059] Relative to the maximum power P_(max), the thickness of themicrostructure h must be comfortably less than:$h < {\frac{P_{\max}}{2\quad \pi \quad k\quad T_{trim}}.}$

[0060] For example, if P_(max)=100 mW, T_(trim)=700° C. and k=0.014W/cm° K (for silicon dioxide), the thickness h must be less than ˜17 μm.Practically, thickness h should be less than ˜10 μm because (1) theactual size of the heater and trimmed resistor cannot be neglected and(2) the thermal conductivity k for a real (usually multi-layer)structure is normally higher (for example including silicon nitride(k=0.16 W/cm·° K) and polysilicon (k=0.3 W/cm·° K)). Further decrease ofh enables the achieving of higher temperatures in the heated area, for agiven pulse energy.

[0061] One possible configuration of the invented device is shownschematically in FIGS. 2-4. FIG. 2 depicts a two-bridge cantilever 1,serving as a mechanical support for four resistors—two functionalresistors R₁, R₂, and two electrically-heated resistors R_(1h), R_(2h).The resistors are placed on the central area 2 of the cantilever 1. Thecantilever 1 is suspended over the cavity 9, etched in a siliconsubstrate 3, thus thermally isolating the cantilever 1 from the siliconsubstrate 3, which acts as a heat sink. Electrical connections to theresistors 4, 5, 6, 7, pass through two bridges 8 and enter thenon-thermally-isolated region above the silicon substrate 3. FIG. 3gives a cross-sectional view of the micro-machined structure.

[0062] In a preferred embodiment, standard micro-fabrication technologysuch as CMOS (or BiCMOS, or others), is used to fabricate resistive anddielectric layers to form the cantilever. It is well-known that suchdielectric layers as silicon oxide and silicon nitride have low thermalconductivity. Therefore high thermal isolation (approximately 20-50°K/mW) can be achieved for the type of microstructure described here.

[0063] Resistors R₁, R₂, R_(1h) and R_(2h) can be made, for example,from polysilicon having sheet resistance of 20-100Ω/square, which istypical for CMOS technology. It is also known from the prior art thatpolysilicon resistors can be thermally trimmed by heating them up totemperature higher than a certain threshold T_(th), such as T_(th)≈500°C.

[0064] A polysilicon resistor having resistance of 10 kΩ (for example)can be readily fabricated in an area of approximately 30 μm×30 μm, if atechnological process having 1 μm resolution is used. For a 0.8 μm or0.35 μm or smaller-feature-sized process, the size of the resistor canbe significantly smaller. Therefore all four resistors, two functionalwith resistance of, for example, 10 kΩ each, and two auxiliary, withpreferably lower resistance such as approximately 1 kΩ, can befabricated on the thermally isolated area 2 with typical area in anapproximate range of 500 μm²-20,000 μm², e.g. 50 μm×100 μm. This size isreasonable for many possible applications, and releasing of the wholestructure can be done by well-known micro-machining techniques, forexample chemical etching in an isotropic etchant solution(s), orisotropic dry silicon etch techniques.

[0065]FIG. 4 shows schematically one potential layout of resistorsplaced on the cantilever 1. Resistors R₁, 10, R_(1h), 12 and R₂ 11,R_(2h) 13 are embedded and grouped so that the locations of portions ofthe resistive elements in R₁/R_(1h) and R₂/R_(2h) resistors alternatealong the central thermally isolated area 2 of the cantilever 1. Adistance L, shown in FIG. 4 separates these resistive portions from eachother.

[0066] The heater resistors R_(1h) 12 and R_(2h) 13 can be either insideor outside of the functional resistors in the serpentine pattern. FIG. 4shows the heaters on the inside of the pattern. Many potential layoutsare available. In order to help maintain a relatively spatially flatT(x) profile, it may be advantageous to have the heater resistors on theoutside (as shown later in FIG. 12.)

[0067] The device functions as follows. For simplicity of explanation,before a trimming pulse (at t₀), the structure is stabilized atquiescent temperature T=T_(quiescent), as shown in FIG. 4. When a shortpulse of voltage (which can be square or shaped), with duration At isapplied to the resistor R_(1h) 11, a certain amount of heat is injectedinto the restricted resistive regions 14, shown roughly asdiagonally-shaded circles in FIG. 4, corresponding to R₁ and R_(1h),while the restricted areas corresponding to R₂ and R_(2h) 15, (unshadedcircles) remain at or near the quiescent temperature. This situation isrepresented by the plot T(x) at time t₁, (at the end of the pulse), inFIG. 4 (Qualitative Dynamic Temperature Distribution). Quantitatively,the overheating temperature of these particular locations can beestimated as (T_(max)−T_(quiescent))=(PΔt)/C, where P is dissipatedpower and C is thermal capacity of the heated location. Thisapproximation is valid only for short-enough pulses (dynamically pulsedcases (c) and (d)). To evaluate preferable pulse duration, the followingsuggestions can be made. During time t_(T), heat is transferred alongthe cantilever to a certain distance L defined by equation: t_(T)=L²/2χwhere thermal diffusivity χ=k/ρc_(v); k is thermal conductivity; ρ isdensity and c_(v) is specific heat of the material of the cantilever.Therefore, if L is the distance between the heated locations 14, and“cold” locations of the non-trimmed resistor 15, the duration of thepulse Δt should be preferably less than time t_(T). This means thatheating of the resistor R₁ 10 is terminated before heat reaches resistorR₂ 11. After the end of a pulse, the accumulated heat further spreadsover the structure yielding more uniform temperature distributions overtime. Temperature distributions T(x) along the structure at timest₂<t₃<t₄, corresponding to this case, are also shown schematically inFIG. 4. The overall temperature is also decreasing toward T_(quiescent),as the heat is transferred away to the ambient and substrate. Theimportant feature of the described trimming cycle is that thetemperature at the locations R₂/R_(2h) never exceeds the trimmingthreshold temperature T_(th). Therefore only resistor R₁ 10 is beingtrimmed. Analogously, resistor R₂ 11 can be trimmed independently,without trimming of the resistor R₁ 10. Estimation of the trimmingprocess of a polysilicon resistor placed on a cantilever between silicondioxide layers (which is typical for traditional CMOS technology) anddistance L=20 μm between “hot” and “cold” locations, gives anapproximate pulse duration Δt less than 0.4 ms (k=0.014 W/cm° K; ρ=2.19g/cm³; c_(v)=1.4 J/g·°K for silicon dioxide; (R. S. Muller, T. I.Kamins. Device electronics for integrated circuits John Wiley & SonsInc. NY, Second Edition, 1986.).

[0068] Elements in the prior art (for example D. Feldbaumer, J. Babcock,V. Mercier, C. Chun, Pulse Current Trimming of Polysilicon Resistors,IEEE

[0069] Trans. Electron Devices, 1995, vol. 42, pp. 689-695), indicatesthat trimming to decrease resistance is done by short pulses at hightemperature, and that trimming to increase resistance (recover) is doneby longer heat exposure, at a temperature lower than is needed todecrease the resistance, but higher than the threshold for instability.While the short high-temperature pulses may be readily applied toindependently trim one element without affecting the others, the longerexposure needed to increase resistance (recover) may impose restrictionson the independent trimming of one resistor among a plurality on amicro-platform. To resolve this problem, in such cases the followinguseful algorithm can be outlined: (1) apply long heat exposure at atemperature that increases the resistance, for all trimmable elements onthe micro-platform; (2) measure all of the trimmable resistances; (3)use short pulses at high temperature to independently trim eachtrimmable resistor down to its desired value.

[0070] In general, T_(quiescent) can be different from the ambienttemperature. For example, the situation where T_(quiescent) issubstantially higher than the ambient, but lower than T_(th), may bedesirable in some situations, for management of trimming pulseparameters and available voltage restrictions. For example, ifT_(th)>>200° C. and if T_(quiescent)≈200° C., which can be obtained byeither DC heating or an appropriate ratio of pulse-width to pulse-period(e.g. ½), then the local overheating would need only to be (T_(th) −200°C.), to initiate trimming. As a result, the trimming pulse amplitudesmay be lower than they would need to be if T_(quiescent) were at or nearto room temperature.

[0071] For many applications, a combination of resistors R₁ 10 and R₂ 11may be used as a divider (for example, R-R or R-2R dividers) or atrimmer-potentiometer. The stability of these devices may be made to bevery high even if the resistors have a non-zero TCR, as long as they areoperating at the same (common) temperature. However, if the tworesistors are operated at different dissipated powers (as they often maybe), the difference in dissipated electric power may result in differentelevated temperatures of the resistors R₁ 10 and R₂ 11 placed on amicrostructure. For example, if the TCR of the resistors is 0.001/° K, atypical value for highly-doped polysilicon, then a temperature imbalanceof 0.001° K will give a resistance mismatch of 1 ppm. This effect willbe especially important on a device having high thermal isolation, wherelarge temperature imbalances would be likely, even for moderatefunctional current levels.

[0072] To suppress or minimize this effect, distributed alternatingpackets of resistance are proposed in this invention. Small packets ofR₁/R_(1h) and R₂/R_(2h) are alternated at least 2 times in order for thetwo functional resistors to share the heat dissipated in either one bythermal conductance across the structure. In this case, even whendifferent power densities are dissipated in the two functionalresistors, the temperature imbalance of the two resistors isdramatically reduced. This situation is schematically depicted at thebottom of FIG. 4 (Qualitative Static Temperature Distribution), wherethe temperature non-uniformity is small, and all temperatures arecomfortably below T_(th). To improve thermal conductance through themicrostructure for better temperature equalization at steady stateconditions, additional material 16 with preferably high thermalconductivity and relatively high thermal mass per unit area can beplaced near and between the locations of the trimmable functionalresistors. Polysilicon, for example, can be used for this purposebecause it can withstand high temperature during trimming.

[0073] Efficient layout of the invented device must satisfy twoconstraints/imperatives, which may be partly contradictory: (1) thermalisolation between the resistors R₁ 10 and R₂ 11 during dynamic heating(trimming) and (2) high thermal equalization between these resistorsduring operation at slowly-changing or DC dissipated power levels. FIG.5 shows one possible configuration of the structure. Slots 17 betweenheated 14 and non-heated areas 15 reduce heat transfer and increasethermal isolation between the resistors R₁ 10 and R₂ 11 during trimming.During operation at DC or slowly-varying conditions, heat spreadsthroughout the structure by the paths on both sides of the slots 17. Tomake this heat transfer more efficient under DC or slowly-varyingconditions, additional material 16 with preferably high thermalconductivity is placed on the structure. Usage of these slots allowscloser location of two functional resistors that reduces the size of themicrostructure and may simplify its fabrication/etching.

[0074] In general, the designer of the device can vary layout parameterssuch as the distance L between trimmed areas 14, width of themicrostructure 2, size of the slots 17 size and thickness of elements 16made from highly thermally-conductive material and level of thermalisolation of the whole microstructure 1 to optimize operation andtrimmability of the device.

[0075]FIG. 6 shows schematically an additional embodiment of the heaterand trimmed resistor with thermal isolation between trimmed andnon-trimmed resistors provided by continuous slots 17.

[0076] It is known from prior art that the trimming magnitude ΔR_(trim)can be quantitatively presented as:$\frac{\Delta \quad R_{trim}}{R_{0}} = {{F\left( {T_{trim} - T_{th}} \right)}\quad {\varphi \left( t_{trim} \right)}}$

[0077] where R_(o) is the initial resistance of the trimmed resistor.Note that functions F(T_(trim)−T_(th)) and φ(t_(trim)) are in principlenon-linear. For example, as was described in Canadian MicroelectronicsCorporation Report #IC95-08 September 1995, p. 91, a 30% increase ofdissipated power (from 14 mW to 20 mW) in a thermally isolatedpolysilicon resistor, results in dramatic acceleration of trimming.Understanding and judicious use of this feature of the thermal trimmingprocess is essential for its optimization and reduction of requiredenergy (important in battery-powered applications) (e.g. a subtle risein delivered power/trimmed temperature) may result in substantiallyshorter trimming exposure t_(trim). Trimming non-linearity is alsoimportant to reach not only fast but also accurate trimming. Thisfeature can be used in such a manner that rough and fast trimming/tuningis done at one trimming temperature at the beginning of tuning. Then,fine and comparatively slow tuning can be done at another (possiblylower) trimming temperature (T_(trim)>T_(th)). Furthermore, thedirection of trimming (increase vs. decrease) may depend sensitively onT.

[0078] The invented concept of dynamic thermal trimming requires shorttrimming pulses with duration less than the heat propagation timebetween trimmed and non-trimmed local areas of the microstructure. Pulsewidth Δt is also substantially shorter than the characteristic timerequired to reach temperature equilibration with the ambient. Thereforetypical reaction of the trimmed region to a rectangular voltage pulsemay be presented as shown schematically in FIG. 1c. Note that thetrimming time is significantly shorter than pulse width. To (1) improveenergetic efficiency of trimming by increasing of trimming time duringeach trimming pulse and (2) provide better control of trimmingtemperature, trimming pulse with optimized waveform is proposed (seeFIG. 1d). At the beginning of the pulse, voltage amplitude issubstantially higher than averaged through the pulse to reach trimmingtemperature quickly. Then voltage amplitude is reduced so that deliveredpower compensates heat loss due to heat leakage into ambient andmaintains trimming temperature at a predetermined value. Temperaturecontrol during trimming is important to reach desired rate of trimmingand provide rough/fast and fine/slow resistance tuning. Besides reversetrimming described in (D. Feldbaumer, J. Babcock, Theory and Applicationof Polysilicon Resistor Trimming“, Solid-State Electronics, 1995, vol.38, pp. 1861-1869) in the case of polysilicon, in general, resistortrimming at higher temperatures can be realized only when the trimmingtemperature is appropriately controlled (as shown in FIG. 1d, not 1 c).

[0079] Another issue raised in the invention is immunity of the balancedresistors R₁ 10 and R₂ 11 to temperature gradients across the siliconsubstrate 3, which may result from side heat sources located on the samechip or even outside the chip or its packaging. As was explained before,a difference in operating temperature of the resistors R₁ 10 and R₂ 11,which may have in general non-zero TCR, results in their imbalance anddegrades the long-term stability of the device. This invention providesat least three mechanisms for reduction of the effects of suchacross-chip temperature gradients. The first mechanism is that Area 2 isthermally isolated from the substrate 3 and therefore has lowersensitivity to temperature gradients across the chip. The secondmechanism is that temperature equalization by alternating resistancepackets placed on an area. 2, described above further improvesinsensitivity to across-chip temperature gradients. For the thirdmechanism, FIG. 7 shows one of the bridges 8, a portion of themicrostructure 1. Electrical lines 5 and 6 are connected to theresistors R₁ 10 and R₂ 11. Temperature differential ΔT_(o) at the borderof the cavity 9 caused by non-uniform heating of the substrate 3 can beminimized by reducing separation between the two connection lines 5 and6 to the range of a few microns or less. Moreover, the temperaturedifferential ΔT₁ at a certain distance from the cavity 9 edge will beeven smaller than ΔT_(o) because of heat transfer across the bridge 8.

[0080] Therefore, the placing of two matched resistors R₁ 10 and R₂ 11on a thermally isolated microstructure 1 with small spacing betweenelectric contact lines 5 and 6 and alternated location of R₁/R_(1h) andR₂/R_(2h) areas provides substantial immunity to temperature gradientsacross the substrate 3.

[0081] Another method of temperature equalization of the resistors R₁ 10and R₂ 11 can be used, if the proportion of dissipated power on each ofthem during operation is known, for example for an R-2R divideroperating with the same current passing through both functionalresistors. In this case the resistor with higher dissipated power (2R)can be located on the cantilever so that its thermal isolation from thesilicon substrate is less than for the resistor with lower dissipatedpower (R). As an example, FIG. 8 shows schematically one possible layoutof an R-2R divider with the resistor R₂ 11 having higher resistance thanresistor R₁ 10. Resistor R₂ 11 is placed near the edges of thecantilever and closer to the silicon substrate than the resistor R₁ 10.Therefore its has better thermal contact with silicon substrate. If thepower dissipated in the resistor R₂ 11 is two times higher than in theresistor R₁ 10, and if the layout of the suspended microstructureprovides two times higher thermal isolation for the resistor R₁ 10 thanfor the resistor R₂ 11, then the elevated temperature of both resistorswill be almost the same. Close proximity on the cantilever, as well asthe alternating resistive packets, will further help to equalize theoperating temperature of two resistors. This approach can be used toprovide close operating temperature of two resistors, matched accordingto some ratio (not necessarily 2:1).

[0082] On the other hand, one can also co-design a pair ofmicro-platforms to attain closely-matched temperatures during operation.One such alternative layout consists of two resistors located on twodifferent thermally isolated membranes (for example over a commonmicro-machined cavity). Such a layout may be preferable in somecircumstances, for example when both lower trimming power is desired (DCtrimming) and simpler requirements to temperature imbalance duringoperation are applicable. In some circumstances, even placement of thepairs of resistors (where each pair consists of one functional 10, 11and one heating 12, 13 resistor), on a separate microstructure 1 asshown in FIGS. 9 and 10, may offer certain benefits (may be preferablein some applications). As an example of a benefit: the structure may betrimmable by a DC signal, (without short pulses), simplifying thetrimming procedure. The T-stability might not be as good, but might besufficient for some applications. Two separate microstructures 1 shownin FIGS. 9 and 10 are suspended over the cavity 9 in a semiconductorsubstrate and have different supporting bridges 8. The differencebetween these two layouts is that the bridges 8 in the second one (FIG.10), are placed closer to each other which is preferable, whentemperature gradients are induced in the substrate, as has beenexplained above.

[0083]FIG. 11 shows schematically the layout of a trimmable R-2R dividerwith two pairs of functional 10, 11 and heating 12, 13 resistors placedon separate cantilevers 1 suspended over the cavity 9 in the substrate.If the power dissipated on the resistor R₂ 11 (2R) during operation istwo times higher than the power dissipated on the resistor R₁ 10 (R),the preferable layout should provide thermal isolation of the resistorR₁ 10 (R) two times higher than that of the resistor R₂ 11 (2R). In thiscase, the (elevated) temperatures of the two functional resistors wouldbe almost the same, yielding a stable resistor divider, even though theabsolute resistance might be varying.

[0084] It should be noted that the resistances within the restrictedresistive regions need not be side-by-side on the microstructure.Instead, they may be arranged to be one over the other, as long as theelectrical insulation between them is sufficient.

[0085] As alluded to above, the trimming behavior at temperatures abovethe trimming threshold may be a complex and sensitive function of T.Thus, for accurate control of trimming in the functional resistor, it isimportant for the entire functional resistive element being trimmed tobe maintained at the same (and controllable) temperature. Thus thespatial T profile, T(x) in the heat-targeted region, should be constant.However, since the heat-targeted element, even in steady state, isintended to be at a higher T than its surroundings, the boundaries ofthe heat-targeted region will tend to be at a temperature lower than theT at the center. In order to compensate for this, FIGS. 12a, 12 b, and12 c show examples of layouts intended to dissipate more power at theedges of the heat-targeted region. More power can be dissipated at theedges of the heat-targeted region by increasing the resistive patharound the perimeter, and/or increasing the resistivity of the elementsat the perimeter. Since the direction of trimming depends sensitively ontemperature, it is preferable to have a major portion of the functionalresistor having a flat temperature distribution so that most of the bulkof the resistive element is trimmed in the same direction. Therefore, apower dissipation geometry for the heating element can comprisesupplying more heat around the edges of the functional resistor in orderto counteract a faster heat dissipation in the edges and resultingtemperature gradients across the thermally-isolated micro-platform.

[0086] One can place the functional and heating elements on a moveablemicro-platform or micro-structure, such that during operation it is inthermal contact with the substrate, to attain lower overheatingtemperatures and such that during trimming it is thermally isolated(using lower power). FIG. 13 shows one such configuration.

[0087] Trimming potentiometer. FIG. 14 shows schematically theelectrical connection of two resistors R₁ 10 and R₂ 11. Their resistancecan be thermally trimmed by two electrically isolated heating resistorsR_(1h) 12 and R_(2h) 13, as has been explained above. High thermalisolation of the resistors shown in FIGS. 1-12 allows trimming bydissipating electric power as low as 10-30 mW (say, 5V and 2-6 mA). Asubstantial difference of the proposed trimming potentiometer (trimpot)from digital potentiometers available on the market is the following:While a digital potentiometer allows discrete variation of resistance(usually, not more than 256 steps=0.4%), the invented trimpot providescontinuous tuning with much higher accuracy than 0.4%. For example, twopolysilicon resistors in a prototype device manufactured in a standard1.5 μm CMOS process have been repeatedly thermally trimmed with accuracyof better than 5 ppm (5·10⁻⁶). Their initial imbalance aftermanufacturing was approximately 1%. The resistance of these polysiliconresistors was found to be trimmed by as much as approximately ±15% oftheir initial value.

[0088]FIGS. 15 and 16 show schematically two possible embodiments ofthree-element thermal sensor (e.g. thermo-anemometer, thermalaccelerometer), with two functional thermally trimmabletemperature-sensitive elements R_(S1) 19 and R_(S2) 20 with accompanyingheaters R_(S1h) 21 and R_(S2h). The thermal sensor also contains thefunctional heater R_(HEAT) 18 placed between two temperature-sensitiveelements 19 and 20. All functional elements 18, 19, 20 and auxiliaryheaters 21 and 22 which may be manufactured, for example, frompolysilicon, are disposed on one thermally isolated platform (FIG. 15)analogous to those described in U.S. Pat. No. 4,478,077. Modification ofthe shapes of openings to the cavity 9 and slot 17 (top view) transformsone platform into three separate ones shown on FIG. 16 with bettermutual thermal isolation of functional elements. For both structuresshown on FIGS. 15 and 16, the disclosed method of trimming of functionalresistors R_(S1) 19, R_(S2) 20 can be applied. Note that higher mutualthermal isolation of functional resistors in the second structure (FIG.16) may not guarantee unwanted trimming of the central heater R_(HEAT)18 during the trimming of one of the resistors R_(S1) 19 or R_(S2) 20.Therefore the same considerations (precautions) must be taken inchoosing of the parameters of the pulsed thermal trimming process.

[0089] In general, this invention is applicable to any existing trimmingprocess done by a manufacturer in a variety of electronic devices, wherethese resistors are used as functional elements. For example, suchtrimmed resistors may be used in analog-to-digital converters,digital-to-analog converters, reference voltage sources, operational andinstrumentation amplifiers, resistor networks and other devices. Theaccuracy of trimming can be very high, exceeding accuracy given by lasertrimming. In addition, the realization of the invented technique doesnot require special equipment (powerful laser) and can be easilyautomated using common electrical equipment such as voltage sources andcontrollers. Trimmable resistors can be manufactured in a standard CMOS(or BiCMOS) process that allows their integration in integratedcircuits.

[0090] In addition to the above well-known possible applications knownfrom the prior art, the invented trimming technique can be used in a new“user-oriented” group of applications, characterized by low electricvoltage and power required to initiate trimming. This enables variouslevels of user to perform trimming of electronic components. This couldbe during assembly of complex electronic systems (tuning, adjustment,regulation of voltage offset and amplification, etc.), and manuallyand/or automatically initiated during operation of a system to provideadaptive regulation/tuning.

[0091] Offset voltages in operational and instrumentation amplifierstypically result from variations of ambient temperature, varyingtemperature gradients, aging effects and other reasons, causingimbalance of the input cascade of the amplifier. Note that turning theamplifier on results in its self-heating and inevitable drift of offsetvoltage during period of time from tens of seconds to several minutes.Balancing of the amplifier by an external trimpot helps to reduce offsetvoltage but cannot eliminate its drift during operation. Use of theinvented thermally activated trimpot (as an integrated part of theamplifier or as a separate component electrically connected to theamplifier) allows automatic adaptive regulation of offset voltage. Onepossible algorithm for this balancing consists of, (1) the input of theamplifier must be temporarily disconnected from the input voltagesource; (2) zero voltage should be applied to input; (3) output voltageis measured, (4) thermal trimming is activated to minimize offset outputvoltage; (5) input signal is fed to the amplifier again. The differencebetween this invented offset voltage regulation and the use of a chopperamplifier is that in this invention this chopping-like scheme needs onlyto be activated for short periods of time, allowing the amplifier tofunction in a non-chopped manner for the rest of the time. In this case,the usual continual noise induced by chopping is not present. In thiscase, one achieves the benefit of near-zero-offset operation, withoutthe noise penalty of the chopping. Such a scheme can be used inconjunction with an on-board T-sensor, allowing intelligent managementof trimming events: frequent trimming need only be initiated duringperiods of rapid temperature change, such as at turn-on, or any othercase of rapidly-changing environment (such as the user pulling the cellphone out of the pocket outdoors during winter).

[0092] The invented technique can be used in amplifiers withprogrammable gain. In currently typical amplifiers, gain is regulated ina discrete manner by switching of appropriate resistors in an array.Thermally trimmed resistors would allow continuous tuning of gain.

[0093] If functional resistors R₁ 10 and R₂ 11 (and perhaps moreresistors) are sensing elements in a sensor, and the sensor outputsignal essentially depends on their resistance, the invented trimmingtechnique can be applied. For example, thermally trimmed resistors canbe a part of thermo-anemometers or thermal accelerometers or pressuresensors, such as in FIGS. 15, 16. This method can be used to trimdevices and structures similar to those variations described in U.S.Pat. Nos. 4,472,239 and 4,478,076. Those micro-machined structurescontain a plurality of thermo-resistors placed on a suspendedthermally-isolated plate having various configurations of slots andopenings. The resistors in those and similar sensors and layouts couldbe altered, to be made from a material suitable for the trimminginventions herein, (for example, from polysilicon or other materialswhich allow thermal trimming). In this case, the methods (dynamicsquare- and shaped-pulses) invented herein would allow selectivetrimming of (a) certain thermo-resistor(s) without affecting others.

[0094] A variety of levels of performance and result would be available:(1) Pulsed trimming of a particular resistor by directly applying anelectric signal to the resistor itself. One would need to beware thatthe heating of the particular resistor did not unbalance a closelyadjacent resistor (for example, since the adjacent resistor might be theresistor which provides the heat for operation of the thermal sensor(for example, thermo-anemometer), whose performance relies on thesymmetry of its heat dissipation). (2) One may increase the width ofslots and/or separation of the thermo-resistors, to attain better mutualthermal isolation between the thermo-resistors, making longer pulsesuseable for trimming. This may reduce to very large separations orslots, (which may be equivalent to placing the resistors on separatemicro-platforms), or may take the form of actually placing thethermo-resistors on separate micro-platforms, and trimming themseparately. (3) One may incorporate separate heating elements forheating of the targeted thermo-resistors as described above in thisinvention, allowing trimming under a wider range of conditions.Electrically isolated heating resistors like R_(1h) 12 and R_(2h) 13 (ormore) can be used for trimming as was explained before. In general,depending on mutual thermal isolation, one varies the pulse duration andshape. Also in general, the preferable layout of the resistors shouldprovide an overall high level of thermal isolation to reduce electricpower required for trimming and selective trimming.

[0095] Usage of the invented technique in sensor applications allowsadaptive tuning/balancing of the sensor during operation, which can bedone automatically. For example, periodic balancing (offset regulation)of a thermoanemometer-type flow sensor in a mass-flow controller can bedone during operation when gas/liquid flow is interrupted for a shortperiod of time. The same approach can be implemented in othersensor-based systems if zero input signal can be applied to the sensorfor a certain period of time.

[0096] Sensors containing thermally trimmed resistors and sensor modules(containing sensors and accompanying electronics) can be tuned using theinvented technique, by a sensor manufacturer or system manufacturer. Inthis case, manually adjusted and potentially unreliable mechanicalpotentiometers can be eliminated.

[0097] The concept of a precision resistor with near-zero TCR consistingof two parts with negative and positive TCR is known from prior art(U.S. Pat. No. 6,097,276). Manufacturing of such a resistor includesseveral stages of laser trimming of both resistive parts with subsequentmeasurement of resistance at different temperatures. The inventedthermal trimming technique can be applied to substitute laser trimming,improve accuracy of matching of two resistive parts and simplifymanufacturing processes. In accordance with a general concept, aprecision resistor contains two functional resistors R₁ 10 and R₂ 11 andtwo heating resistors R_(1h) 12 and R_(2h) 13 placed on thermallyisolated supporting mechanical microstructures as described above. Oneof the functional resistors, say, R₁ 10 has positive TCR and another, R₂11, has negative TCR. Types of material of these resistors are notspecified but as an example, polysilicon can be used for this purpose.It is known that TCR of polysilicon depends on doping and can bepositive (approximately +10/⁻³/° K) at high doping level and negative(from −10⁻⁴/° K to several −10⁻³/° K) at low doping. Therefore thermaltrimming of two resistors can be done so to provide target value oftotal resistance and zero total TCR. It should be noted that periodicheating of the resistor required to measure its TCR during manufacturingprocess before and after trimming does not require external heat sources(hot plates or ovens) and can be done by heating resistors R_(1h) 12 andR_(2h) 13. Obviously, the elevated temperature in this case should bemuch lower than for thermal trimming purposes. An additional convenienceof usage of heating resistors R_(1h) 12 and R_(2h) 13 is that heatingand cooling can be performed very fast, with typical time of 20-50 msdefined by thermal inertia of the microstructure. Note that the sameheating and trimming could be provided from another heat source, such asa laser, or self-heating of the functional resistor itself. In thesecases also, the heating and cooling times will be determined by thethermal inertia of the micro-platform, as discussed above. Therefore thewhole manufacturing process can be substantially faster. For manyapplications, accurate knowledge of temperature behavior of TCR isrequired, including terms of higher-order variation with temperature.This requires measurement at a plurality of elevated temperatures. Asanother example, one could self-heat a functional resistor up to a knownrelatively high temperature (still substantially below the trimmingtemperature), and then measure its resistance several known times as itcooled to room temperature at known cooling rate. The invented techniqueallows also reduction of number of rejected resistors and improvestechnological yield because thermal trimming may be reversible. Usage ofCMOS-compatible materials such as polysilicon with different dopinglevels allows integration of such precision resistors in integratedcircuits.

[0098] More generally, the placing of functional elements onthermally-isolated micro-platforms having small thermal mass, allows theacceleration of the process of measurement of its physical parameters,if these measurements require measurement at one or more elevatedtemperatures (of course, still well below the thresholds for trimming orrecovery). Note that these measurements can be used in many processes ofcalibration or trimming.

[0099] It will be understood that numerous modifications thereto willappear to those skilled in the art. Accordingly, the above descriptionand accompanying drawings should be taken as illustrative of theinvention and not in a limiting sense. It will further be understoodthat it is intended to cover any variations, uses, or adaptations of theinvention following, in general, the principles of the invention andincluding such departures from the present disclosure as come withinknown or customary practice within the art to which the inventionpertains and as may be applied to the essential features herein beforeset forth, and as follows in the scope of the appended claims.

1-25. (Canceled)
 26. A circuit for trimming a functional resistor, thecircuit comprising: a plurality of functional resistorsthermally-isolated on a substrate; and trimming circuitry for subjectinga portion of the substrate to heat pulses such that a resistance valueof one of said plurality of functional resistors is trimmed while aresistance value of remaining, ones of said plurality of functionalresistors remains substantially untrimmed.
 27. A circuit as claimed inclaim 56, wherein said trimming circuitry comprises circuitry forpassing a signal through said one of said plurality of functionalresistors.
 28. A circuit as claimed in claim 56, wherein said trimmingcircuitry comprises at least one heating resistor on said micro-platformfor receiving a signal and trimming said one of said plurality offunctional resistors.
 29. A circuit as claimed in claim 28, wherein eachof said at least one heating resistor traces at least one of saidplurality of functional resistors.
 30. A circuit as claimed in claim 29,wherein a first pair of functional resistor and heating resistor isgrouped and embedded with a second pair of functional resistor andheating element so that locations of portions of said first pair andsaid second pair alternate on said thermally-isolated micro-platform.31. A circuit as claimed in claim 30, wherein said portions of saidfirst pair and said second pair are separated by slots in saidthermally-isolated micro-platform, thereby reducing heat transfer andincreasing thermal isolation between said first pair and said secondpair.
 32. A circuit as claimed in claim 31, wherein said slots arecontinuous.
 33. A circuit as claimed in claim 56, wherein said trimmingcircuitry comprises circuitry for transmitting a plurality of electricalpulses and measuring said resistance value of one of said plurality offunctional resistors in between each of said plurality of electricalpulses to determine whether a target resistance value has been obtained.34. A circuit as claimed in claim 56, wherein said trimming circuitrycomprises circuitry for transmitting dynamically-shaped pulses toachieve substantially constant temperature as a function of time duringa trimming pulse.
 35. A circuit for trimming circuit elements, thecircuit comprising: at least two resistive elements with non-zerotemperature induced drift thermally-isolated on substrate, such thatsaid at least two resistive elements are subjected to a substantiallysame operating environment, at least one of said at least two resistiveelements being thermally trimmable; and trimming circuitry for thermallytrimming said at least one of said at least two resistive elements;wherein said at least two resistive elements are connected together insaid circuit in a manner to compensate for said operating environmentand heat generated is distributed among the at least two circuitelements such that an effect of temperature drift is compensated.
 36. Acircuit as claimed in claim 57, wherein said at least two resistiveelements are connected together in series and an applied voltage isdivided with a predetermined ratio.
 37. A circuit as claimed in claim57, wherein said at least two resistive elements are temperaturesensitive elements located closely on said at least onethermally-isolated micro-platform, and whose signals are combined tomeasure a temperature differential.
 38. A circuit as claimed in claim57, further comprising a heating resistor on the at least onethermally-isolated micro-platform in close proximity to said at leastone resistive element, wherein said trimming circuitry further circuitryfor passing a signal through the heating resistor to increase itstemperature significantly for the purpose of trimming said at least oneresistive element.
 39. A circuit as claimed in claim 37, wherein saidheating resistor and said at least one resistive element are on separatethermally-isolated micro-platforms.
 40. A circuit as claimed in claim57, wherein said trimming circuitry for heating further comprisescircuitry for transmitting a plurality of electrical pulses andmeasuring said resistance value of one of said at least two resistiveelements in between each of said plurality of electrical pulses todetermine whether a target resistance value has been obtained.
 41. Acircuit as claimed in claim 57, wherein said trimming circuitry forheating comprises circuitry for transmitting dynamically-shaped pulsesto achieve substantially constant temperature as a function of timeduring a trimming pulse.
 42. A circuit for trimming a functionalresistor, the circuit comprising: a functional resistor on substratesubject to a heat source having a power dissipation geometry adapted toobtain a substantially constant temperature distribution across saidfunctional resistor when a temperature of said functional resistor israised for trimming purposes; and trimming circuitry for trimming thefunctional resistor.
 43. A circuit as claimed in claim 58, wherein saidheat source comprises a heating resistor on said thermally-isolatedmicro-platform in close proximity to said functional resistor, andwherein said trimming circuitry comprises circuitry for passing a signalthrough said heating resistor to trim said functional resistor.
 44. Acircuit as claimed in claim 58, wherein said power dissipation geometrycomprises a heater path that encircles the functional resistor.
 45. Acircuit as claimed in claim 58, wherein said power dissipation geometryfurther comprises a heater path that provides more heat to edges of thefunctional resistor and resulting temperature gradients across the atleast one thermally-isolated micro-platform.
 46. A circuit as claimed inclaim 58, wherein said power dissipation geometry comprises a heaterpath that substantially encloses said functional resistor with saidheating resistor.
 47. A circuit as claimed in any one of claims 58,wherein said power dissipation geometry further comprises an increaseddensity of resistive lines near locations where there is greater heatloss to compensate for the heat loss.
 48. A circuit as claimed in claim58, wherein said trimming circuitry for heating comprises circuitry fortransmitting a plurality of electrical pulses and measuring saidresistance value of one of said plurality of functional resistors inbetween each of said plurality of electrical pulses to determine whethera target resistance value has been obtained.
 49. A circuit as claimed inclaim 58, wherein said trimming circuitry for heating comprisescircuitry for transmitting dynamically-shaped pulses to achievesubstantially constant temperature as a function of time during atrimming pulse.
 54. A circuit for calculating a temperature coefficientof resistance of a functional resistor, the circuit comprising: afunctional resistor on thermally isolated on a substrate; heatingcircuitry for injecting a heat pulse to raise a temperature of saidfunctional resistor to a predetermined temperature; measuring circuitryfor measuring a resistance value of said functional resistance at aplurality of temperatures; and calculating circuitry for calculatingsaid temperature coefficient of resistance based on said resistancevalue at said temperatures.
 55. A circuit as claimed in claim 59,wherein said heating circuitry comprises a heating resistor on said atleast one thermally-isolated micro-platform for passing a signal throughsaid heating resistor and heating said functional resistor.
 56. Acircuit as claimed in claim 26, further comprising a thermally-isolatedmicro-platform on said substrate, and wherein said Plurality offunctional resistors are on said thermally-isolated micro-platform. 57.A circuit as claimed in claim 35, further comprising at least onethermally-isolated micro-platform on said substrate, and wherein said atleast two resistive elements are on said at least one thermally-isolatedmicro-platform.
 58. A circuit as claimed in claim 42, further comprisinga thermally-isolated micro-platform on said substrate, and wherein saidfunctional resistor is on said thermally-isolated micro-platform.
 59. Acircuit as claimed in claim 54, further comprising at least onethermally-isolated micro-platform on said substrate, and wherein saidfunctional resistor is on said at least one thermally-isolatedmicro-platform.